Safe Leader-Follower Density Control via Higher-Order Mean-Field Control Barrier Functions

Abstract

Mean-field control barrier functions (MF-CBFs) enforce safety of large-scale multi-agent systems at the level of densities, but existing formulations require the control to act directly on the population to be kept safe. We consider populations that are not directly actuated and are influenced only through other, controlled populations, possibly in the presence of diffusion. We show that if the constrained population lies at directed graph distance d from the actuated one, then, under a nondegeneracy condition, the safety functional has relative degree d+1 and the control enters its (d+1)-th time derivative affinely. Higher-order safety constraints can therefore still be enforced through a convex quadratic program. We apply the framework to leader-follower density control among dangerous regions, where the follower safety functional has relative degree two and the leader safety functional has relative degree one. We characterize exactly when the two constraints are jointly infeasible and bound the tracking errors induced by the safety correction. Simulations in cluttered environments show that the proposed filter preserves follower safety, whereas enforcing leader safety alone does not.